How can $x$ be in the limit after $x\to\infty$?
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DirkMay 7 '12 at 20:57

@TMM: Yes, actually for $a\in\mathbb{C}$ and $b\in\mathbb{R}$ (as is easy to generalize from the case $a=b=1$), $$\lim_{x\to\infty}\left(1+\frac{a}{x}\right)^{bx}=e^{ab}\,.$$ I was using the special case $a=b=-1$. To get the general formula starting with $a=b=1$, first introduce the $b$ and use that the function $x\to x^b$ is continuous. Then to indroduce the $a$, use the substitution $x\leftarrow \frac{x}{a}$.
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bginsMay 7 '12 at 21:04

@bgins: You are missing the point. $(1 - 1/x)^{-x} \to e$ and not $e^x$.
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TMMMay 7 '12 at 23:09